Towing with a midsize Chevy

Welcome. And sounds like an awesome trip. 
My only advice is if youre at all worried about towing 4klbs with a 7klb rated truck then maybe rethink the towing game altogether. 
MPG? Lol. You said you own both of these but you don’t know what gas mileage it gets? See above recommendation. 
Now, sarcasm aside the only real concern with that rig is the transmission. 
8L45s are a pile of junk. Just like all the GM 8L truck variants. Why they still use them is beyond me. 
Not because you need a new truck or a full size but if you have a smooth shifting good running 8L45 the best thing to do is shine it up good and sell it. Seriously. 
And as far as new/newer GM half tons go, they have become the Dodge of half tons and Ram is now hands down the most reliable.

Ive put lots of miles and hard miles on about every half ton pickup model of the big 3 over the last 30 years. 30-40k miles a year every year.  Mostly all new or newer half ton trucks.  Company rigs so I drive them for a year or 2 or 6 months, sometimes tow more then they’re rated for sometimes flat pedal for 6 hours at the speed limiter.  Plus responsible for fleets of the same trucks.  So I see what works what doesn’t and what lasts  

This coming from someone with 2GMs a Dodge and a Ram in the driveway. I’ve been a GM fan forever and select Chrysler products and I wouldn’t own a new GM half ton unless it was $20k off sticker. 
If you’re set on a half ton, all the newer F150s are pretty solid (honest opinion as I am not a Ford fan), although my last Ford ‘24 F150 5.0 was a lemon. Trans issues from day 1. 
GM, well, umm yeah. They have 1 good combo and it’s stellar. The baby Dmax with the 10 speed is as solid as it gets. Seriously. Beginning in ‘23 I think, they got even better 300/500 power and fixed all the first model quirks (not bad if buy an early 3.0 but they got better).
The 2.7 turbo 4 banger is the only good gas engine unless you like replacing lifters and valve train parts, still….15 years later. I’m 0 for 3 on Chevy 5.3s in the last 10 years models. BUT they have the 8L90 which is a steaming pile of crap. Just like your much lighter duty 8L45. I chewed one of those up in 25k miles and it never even saw a heavy trailer. 
Now to Ram. They’ve been the most reliable ever since 2015 or whenever they got the 8HP trans. That transmission has been and still is the best of the big 3 longitudinal mount transmissions for over 10 years now. Period. They switched to a twin turbo inline 6 in the half tons (and sports cars) last year. First year reports are good. And a pile of power. A base model Hurricane engine is 420/465 iirc and they’re putting down 540 hp out of the HOs. Same 3 litre motor. That says something. The base model Hurricane half ton Rams with 3.92s are 13sec at 100mph 1/4 mile trucks!

So good question. 
Check your abilities if you’re planning on towing through Mexico. May wanna brush up on some skills. I can’t imagine being not mechanically inclined at all and towing a trailer thru Mexico for weeks. Tools, knowledge are gonna make that more enjoyable or vice versa. 
Regarding your truck. It’ll handle the trailer fine. Not great, it’s a midsize, but acceptably for sure. 
But you would do well to think twice about keeping it and especially about flogging it with the trailer day in day out. 
If you decide to keep it, do a full trans service at a minimum so you’re starting out fresh. And also go tow your trailer up and down a mountain in hot weather first and see how hot the trans gets and how it acts. What you’re proposing is like jumping off a boat 5 miles from shore with the plan to swim in when you’re not sure if you can swim or not.